FIA - NLS Models: Biomass Growth vs. Biomass
JAH
2022-10-25
Background
This document has nls (non-linear least squares) regression fits using the Michaelis-Menten functional form to USFS FIA (United States Forest Service Forest Inventory & Analysis) biomass growth vs. biomass relationships. We use the sum of tree biomass growth increment method for the plot biomass growth (\(G\)) calculation (see supplementary methods). Models are fitted separately by US ecoprovince.
Hypothetically, the entire functional form of the following Michaelis-Menten non-linear model is considered: \(G = (1 + (yr-1990)* ge/100) \times (1 - \alpha \cdot B_l) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\), where \(G\) is the plot level biomass growth calculated as the sum of tree biomass growth increments, \(B_l\) is the calculated proportion of biomass loss over the census interval, \(B_{t1}\) is the plot biomass at the first of two FIA plot tree censuses, \(\Delta PDSI\) is the difference in the growing season (January-August) annual average PDSI values over the FIA plot measurement intervals and a 30-year climate normal (1969-1990), and \(yr\) is the measurement year (all FIA data). Free parameters are \(\alpha\): the growth compensation of lost plot biomass, \(ge\): biomass growth enhancement over time, \(A\): the Michaelis-Menten asymptote and \(k\): the Michaelis-Menten half-saturation constant.
Data have increasing variance in \(G\) with increasing \(B\), Thus, weighted nls is the best approach. We explore a few weighting options and found that proportional weighting can be achieved by weighting observations by \(\frac {1} {meanG}\) in equal-sample sized plot biomass bins (n=20) for each ecoprovince.
Model selection is used to determine. to determine the best fitting models, which is implemented in two parts. A first model selection is done to determine the best model form either including \(\alpha\): the biomass compensation effect due to lost biomass (natural mortality or harvest), \(\phi\): the effect of changing climate (quantified as \(\Delta PDSI\), or both. \(\Delta PDSI\) is defined the difference in the Palmer drought severity index from January - August for the 10 years preceding the biomass measurement and the 1969-1990 period). We explored \(\Delta PDSI\) using only the summer growing months (June-August) over the same intervals, and analyses were insensitive to that change. For the first model selection the following models are considered:
model 1: simple model \(G = (1 + (yr-1990)* ge/100) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
model 2: phi model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
model 3: phi-alpha model \(G = (1 + (yr-1990)* ge/100) \times (1 + \phi \cdot \Delta PDSI) \times (1 - \alpha \cdot B_l) \times \left( \frac {A \cdot B_{t1}} {k+B_{t1}} \right)\)
Then, a second model selection is done using best-fitting model from part 1 and then considering additional \(p\) and \(s\) parameters (individually, and then together) to modify the Micheaelis-Menten functional form. The \(p\) parameter allows for an intercept in the model (i.e., for the model to not be forced through the origin), and the \(s\) parameter increases model flexibility, with \(s\)>1 leading to more-sigmoidal shape.
sub-model a: p form \(pA + \left( \frac {(1-p)A \cdot B_{t1}} {k+B_{t1}} \right)\)
sub model b: s form \(\left( \frac {A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)
sub model c: p and s together \(pA + \left( \frac {(1-p)A \cdot B_{t1}^s} {k^s+B_{t1}^s} \right)\)
NOTE:
This document contains all \(G\) observations that meet our plot based filtering criteria:
- exclude FIA plots in plantation forests
- exclude FIA plots with multiple plot conditions (COND_PROP_UNADJ > 0.95)
- exclude FIA plots non-productive stands (i.e., those with less than 20 ft^3/acre/year timber producing capability; SITECLCD of 7)
- exclude FIA plots in non-stocked stands (i.e., those with STDSZCD of 5)
- exclude FIA plots in non-accessible areas (i.e., private lands etc., COND_STATUS_CD not equal to 1)
- exclude FIA plot visits that are not part of the annual inventories (which also includes FIA plot visits for Phase 3 ozone measurements)
Additionally, in an effort to clean up the data set, we have removed outlier observations, using a quantile threshold approach. We also calculated plot \(G\) using as biomass balance method (see supplementary methods), and the difference between the two methods. Accordingly, we define \(diff_G\) as the difference between tree incremental \(G\) and biomass balance \(G\). We excluded observations which meet the following criteria using a 0.5% quantile (\(QT\)):
case A: where the \(QT\) difference in tree incremental \(G\) is > biomass balance plot G (i.e., > 99.5% \(diff_G\) positive outliers)
case B: where the \(QT\) difference in tree incremental \(G\) is < mass balance plot G (i.e., < 0.5% \(diff_G\) negative outliers)
case C: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., > 99.5% positive outliers)
case D: where the \(QT\) difference in tree incremental \(G\) is > 0 (i.e., < 0.5% negative outliers)
These data set cleaning criteria resulted in the exclusion of 1677 observations.
Below the model fitting procedure is implemented by ecoprovince:
211 - Northeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6803 4993.8
## 2 6802 4979.5 1 14.368 19.626 9.565e-06 ***
## 3 6801 4700.1 1 279.362 404.233 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24896.15
## 2 2 24878.54
## 3 3 24487.57##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.002313 0.142295 0.016 0.987
## phi 0.019566 0.004338 4.510 6.58e-06 ***
## alpha 0.631937 0.029466 21.447 < 2e-16 ***
## A 3.689310 0.107156 34.429 < 2e-16 ***
## k 9.801095 0.673936 14.543 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8313 on 6801 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.761e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_211, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6801 4700.1
## 2 6800 4695.2 1 4.9446 7.1613 0.007467 **
## 3 6799 4694.0 1 1.1736 1.6998 0.192352
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 24487.57
## 2 3a 24482.41
## 3 3b NA
## 4 3c 24482.71##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.003234 0.142270 0.023 0.98186
## phi 0.019635 0.004338 4.526 6.1e-06 ***
## alpha 0.630429 0.029469 21.393 < 2e-16 ***
## A 3.741260 0.112468 33.265 < 2e-16 ***
## k 13.699719 2.063458 6.639 3.4e-11 ***
## p 0.147297 0.051078 2.884 0.00394 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8309 on 6800 degrees of freedom
##
## Number of iterations to convergence: 3
## Achieved convergence tolerance: 5.436e-06summary
- add p model: fits
- add s model: does not fit
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 1038 row(s) containing missing values (geom_path).
plotting 2
212 - Laurentian Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18772 15066
## 2 18767 14987 5 79.84 19.997 < 2.2e-16 ***
## 3 18766 13948 1 1038.75 1397.574 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 64126.34
## 2 2 64018.45
## 3 3 62672.11##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.613447 0.124463 4.929 8.35e-07 ***
## phi 0.029034 0.002734 10.620 < 2e-16 ***
## alpha 0.822583 0.020204 40.714 < 2e-16 ***
## A 2.880787 0.064092 44.948 < 2e-16 ***
## k 13.763371 0.481140 28.606 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8621 on 18766 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 2.821e-06
## (4 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 18766 13948
## 2 18765 13790 1 157.965 214.957 < 2.2e-16 ***
## 3 18765 13818 0 0.000
## 4 18764 13790 1 28.524 38.814 4.762e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 62672.11
## 2 3a 62460.31
## 3 3b 62499.01
## 4 3c 62462.22##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.587555 0.122541 4.795 1.64e-06 ***
## phi 0.029607 0.002709 10.928 < 2e-16 ***
## alpha 0.814647 0.020054 40.623 < 2e-16 ***
## A 3.134793 0.075777 41.369 < 2e-16 ***
## k 29.206857 1.949741 14.980 < 2e-16 ***
## p 0.193257 0.010655 18.138 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8572 on 18765 degrees of freedom
##
## Number of iterations to convergence: 4
## Achieved convergence tolerance: 4.74e-06
## (4 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 1031 row(s) containing missing values (geom_path).
plotting 2
221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7159 7630.8
## 2 7158 7627.7 1 3.01 2.8274 0.09271 .
## 3 7157 7278.5 1 349.23 343.3965 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 29878.52
## 2 2 29877.69
## 3 3 29544.04##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.406513 0.084819 -16.582 <2e-16 ***
## phi 0.006082 0.004503 1.351 0.177
## alpha 0.687050 0.034952 19.657 <2e-16 ***
## A 6.236216 0.163606 38.117 <2e-16 ***
## k 19.977711 1.683017 11.870 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.008 on 7157 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 3.992e-06
## (8 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_221, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_221, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 7157 7278.5
## 2 7156 7212.0 1 66.481 65.964 5.366e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 29544.04
## 2 3a 29480.33
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.435366 0.083176 -17.257 < 2e-16 ***
## phi 0.006702 0.004483 1.495 0.135
## alpha 0.685682 0.034486 19.883 < 2e-16 ***
## A 7.601341 0.369404 20.577 < 2e-16 ***
## k 99.330652 19.960728 4.976 6.63e-07 ***
## p 0.330195 0.020993 15.729 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.004 on 7156 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 5.435e-06
## (8 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 5 rows containing missing values (geom_point).## Warning: Removed 1036 row(s) containing missing values (geom_path).
plotting 2
222 - Midwest Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4867 3972.7
## 2 4866 3964.9 1 7.849 9.6331 0.001922 **
## 3 4865 3691.1 1 273.807 360.8898 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 18011.57
## 2 2 18003.94
## 3 3 17657.45##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.367163 0.173787 -2.113 0.03468 *
## phi 0.021679 0.007424 2.920 0.00352 **
## alpha 0.800963 0.038568 20.768 < 2e-16 ***
## A 4.975276 0.181412 27.425 < 2e-16 ***
## k 31.602813 1.879517 16.814 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.871 on 4865 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.407e-06
## (7 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_222, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_222, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 4865 3691.1
## 2 4864 3599.1 1 91.936 124.25 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 17657.45
## 2 3a 17536.62
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.383203 0.170237 -2.251 0.0244 *
## phi 0.018160 0.007244 2.507 0.0122 *
## alpha 0.792487 0.038011 20.849 < 2e-16 ***
## A 6.608906 0.369952 17.864 < 2e-16 ***
## k 112.210544 14.732460 7.617 3.11e-14 ***
## p 0.179723 0.010121 17.758 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8602 on 4864 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 3.696e-06
## (7 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95673, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -16, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 4 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1053 row(s) containing missing values (geom_path).
plotting 2
223 - Central Interior Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8777 8518.0
## 2 8776 8502.7 1 15.249 15.739 7.329e-05 ***
## 3 8775 8242.9 1 259.861 276.637 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 34239.99
## 2 2 34226.26
## 3 3 33955.74##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.38661 0.08275 -16.76 < 2e-16 ***
## phi -0.02233 0.00542 -4.12 3.83e-05 ***
## alpha 0.64066 0.03630 17.65 < 2e-16 ***
## A 6.47289 0.18128 35.71 < 2e-16 ***
## k 42.04372 2.70957 15.52 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9692 on 8775 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.628e-06
## (3 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_223, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_223, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## model AIC
## 1 3 33955.74
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.38661 0.08275 -16.76 < 2e-16 ***
## phi -0.02233 0.00542 -4.12 3.83e-05 ***
## alpha 0.64066 0.03630 17.65 < 2e-16 ***
## A 6.47289 0.18128 35.71 < 2e-16 ***
## k 42.04372 2.70957 15.52 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9692 on 8775 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.628e-06
## (3 observations deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 3 rows containing missing values (geom_point).## Warning: Removed 1114 row(s) containing missing values (geom_path).
plotting 2
231 - Southeastern Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12343 22303
## 2 12342 22302 1 0.39 0.2176 0.6409
## 3 12341 19979 1 2323.23 1435.0642 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 60705.76
## 2 2 60707.54
## 3 3 59351.41##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.164562 0.098508 -1.671 0.0948 .
## phi -0.002456 0.004112 -0.597 0.5504
## alpha 0.842236 0.020224 41.645 <2e-16 ***
## A 5.423448 0.112581 48.174 <2e-16 ***
## k 2.780933 0.247040 11.257 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.272 on 12341 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.199e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12341 19979
## 2 12340 19891 1 87.674 54.3911 1.748e-13 ***
## 3 12340 19902 0 0.000
## 4 12339 19891 1 10.595 6.5722 0.01037 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 59351.41
## 2 3a 59299.11
## 3 3b 59305.61
## 4 3c 59301.03##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.186851 0.097467 -1.917 0.0553 .
## phi -0.002130 0.004095 -0.520 0.6029
## alpha 0.840183 0.020110 41.780 < 2e-16 ***
## A 5.596113 0.122987 45.502 < 2e-16 ***
## k 8.774600 1.622335 5.409 6.47e-08 ***
## p 0.390472 0.040679 9.599 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.27 on 12340 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 3.029e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1017 row(s) containing missing values (geom_path).
plotting 2
232 - Outer Coastal Plain Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12467 26614
## 2 12466 26612 1 2.65 1.2433 0.2649
## 3 12465 24215 1 2396.31 1233.5227 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 61666.13
## 2 2 61666.88
## 3 3 60492.17##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.2628008 0.1112158 -2.363 0.0181 *
## phi -0.0005468 0.0045482 -0.120 0.9043
## alpha 0.8349426 0.0213640 39.082 <2e-16 ***
## A 5.4202590 0.1350753 40.128 <2e-16 ***
## k 8.0094796 0.4943964 16.201 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.394 on 12465 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 8.591e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 12465 24215
## 2 12464 23985 1 229.888 119.462 < 2.2e-16 ***
## 3 12464 24056 0 0.000
## 4 12463 23974 1 81.719 42.482 7.407e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 60492.17
## 2 3a 60375.22
## 3 3b 60411.70
## 4 3c 60371.26##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.2904340 0.1092242 -2.659 0.00785 **
## phi -0.0008326 0.0045073 -0.185 0.85345
## alpha 0.8287948 0.0211994 39.095 < 2e-16 ***
## A 5.5132325 0.1680533 32.806 < 2e-16 ***
## k 24.1803371 2.1461877 11.267 < 2e-16 ***
## s 1.3906668 0.1759005 7.906 2.88e-15 ***
## p 0.3791942 0.0308751 12.282 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.387 on 12463 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 8.006e-06summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 953 row(s) containing missing values (geom_path).
plotting 2
234 - Lower Mississippi Riverine Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1262 2732.4
## 2 1261 2730.8 1 1.616 0.7464 0.3878
## 3 1260 2575.7 1 155.141 75.8939 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6239.319
## 2 2 6240.570
## 3 3 6168.582##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.59312 1.11801 1.425 0.154
## phi -0.02501 0.02078 -1.204 0.229
## alpha 0.77337 0.08005 9.662 < 2e-16 ***
## A 3.62885 0.63193 5.742 1.17e-08 ***
## k 9.60975 2.31023 4.160 3.40e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.43 on 1260 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 8.275e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_234, :
## parameters without starting value in 'data': p
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1260 2575.7
## 2 1259 2570.8 1 4.9103 2.4048 0.1212
## model AIC
## 1 3 6168.582
## 2 3a 6168.168
## 3 3b 6168.069
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.60921 1.12275 1.433 0.15203
## phi -0.02576 0.02078 -1.240 0.21524
## alpha 0.76892 0.08010 9.599 < 2e-16 ***
## A 4.13842 0.92838 4.458 9.02e-06 ***
## k 11.64559 6.19571 1.880 0.06039 .
## s 0.61393 0.21272 2.886 0.00397 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.429 on 1259 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.098e-06summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.95842, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.9898, p-value = 6.612e-05
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 948 row(s) containing missing values (geom_path).
plotting 2
242 - Pacific Lowland Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 77 67.216
## 2 76 66.744 1 0.4721 0.5376 0.465679
## 3 75 59.184 1 7.5601 9.5805 0.002764 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 355.9610
## 2 2 357.3970
## 3 3 349.7798##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.29976 1.83293 -0.164 0.870533
## phi 0.06367 0.05197 1.225 0.224338
## alpha 0.86978 0.25121 3.462 0.000888 ***
## A 7.68709 3.17610 2.420 0.017929 *
## k 30.51595 12.20049 2.501 0.014559 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8883 on 75 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 8.21e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_242, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_242, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 75 59.184
## 2 74 51.768 1 7.4154 10.6 0.001707 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 349.7798
## 2 3a 341.0704
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.95258 1.30354 -0.731 0.46723
## phi 0.06990 0.04843 1.443 0.15318
## alpha 0.81225 0.24162 3.362 0.00123 **
## A 22.29721 27.51039 0.811 0.42025
## k 1188.98715 2351.33832 0.506 0.61460
## p 0.20353 0.20959 0.971 0.33468
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8364 on 74 degrees of freedom
##
## Number of iterations to convergence: 12
## Achieved convergence tolerance: 3.221e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.98698, p-value = 0.5974
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -0.45007, p-value = 0.6527
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (geom_point).## Warning: Removed 863 row(s) containing missing values (geom_path).
plotting 2
251 - Prairie Parkland (Temperate)
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1793 1540.0
## 2 1792 1534.1 1 5.9178 6.9128 0.008631 **
## 3 1791 1520.8 1 13.2245 15.5735 8.242e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6619.016
## 2 2 6614.101
## 3 3 6600.552##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.74029 0.26671 -2.776 0.00557 **
## phi 0.02494 0.01059 2.356 0.01858 *
## alpha 0.37760 0.09201 4.104 4.24e-05 ***
## A 4.23533 0.27361 15.480 < 2e-16 ***
## k 22.62163 3.11717 7.257 5.86e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9215 on 1791 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 3.487e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_251, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_251, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1791 1520.8
## 2 1790 1470.0 1 50.831 61.895 6.215e-15 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 6600.552
## 2 3a 6541.499
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.82489 0.25083 -3.289 0.00103 **
## phi 0.02636 0.01038 2.540 0.01117 *
## alpha 0.39463 0.08826 4.471 8.26e-06 ***
## A 19.86974 24.80713 0.801 0.42326
## k 1228.26934 1975.51782 0.622 0.53419
## p 0.10447 0.12488 0.836 0.40299
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9062 on 1790 degrees of freedom
##
## Number of iterations to convergence: 16
## Achieved convergence tolerance: 7.715e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91943, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -10.734, p-value < 2.2e-16
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1176 row(s) containing missing values (geom_path).
plotting 2
255 - Prairie Parkland (Subtropical)
model selection 1
## Error in nls(fg_1, data = G_255, start = c(ge = ge.start, A = A.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_255, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_3, data = G_255, start = c(ge = ge.start, phi = phi.start, :
## number of iterations exceeded maximum of 50
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_255$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_255.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
261 - California Coastal Chaparral Forest and Shrub
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
262 - California Dry Steppe
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
263 - California Coastal Steppe - Mixed Forest and Redwood Forest
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
add p model: does not fit
add s model: does not fit
add s+p model: does not fit
note: model fit, but fit was funky due to data being sparse
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
313 - Colorado Plateau Semi-Desert
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 211 105.125
## 2 210 103.499 1 1.6256 3.2983 0.070777 .
## 3 209 99.344 1 4.1559 8.7433 0.003465 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 498.6817
## 2 2 497.3467
## 3 3 490.5764##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.11494 0.99312 -1.123 0.26287
## phi -0.09677 0.07116 -1.360 0.17533
## alpha 0.81661 0.24529 3.329 0.00103 **
## A 3.47187 1.19369 2.909 0.00402 **
## k 111.42030 36.72779 3.034 0.00272 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6894 on 209 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 2.769e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_313, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 209 99.344
## 2 208 96.499 1 2.8448 6.1318 0.01408 *
## 3 207 94.551 1 1.9482 4.2652 0.04015 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 490.5764
## 2 3a 486.3589
## 3 3b NA
## 4 3c 483.9944##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.15472 0.94108 -1.227 0.221211
## phi -0.09545 0.06806 -1.402 0.162311
## alpha 0.84400 0.23481 3.594 0.000406 ***
## A 2.68538 0.91529 2.934 0.003725 **
## k 109.84363 26.18684 4.195 4.05e-05 ***
## s 2.81887 1.33665 2.109 0.036155 *
## p 0.31531 0.09800 3.218 0.001501 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6758 on 207 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 7.874e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.97558, p-value = 0.0009008
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = 0.018123, p-value = 0.9855
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1103 row(s) containing missing values (geom_path).
plotting 2
315 - Southwest Plateau and Plains Dry Steppe and Shrub
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
321 - Chihuahuan Semi-Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
322 - American Semidesert and Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
331 - Great Plains/Palouse Dry Steppe
model selection 1
## Error in nls(fg_1, data = G_331, start = c(ge = ge.start, A = A.start, :
## number of iterations exceeded maximum of 50
## Error in nls(fg_2, data = G_331, start = c(ge = ge.start, phi = phi.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(fg_3, data = G_331, start = c(ge = ge.start, phi = phi.start, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## model AIC
## 1 1 NA
## 2 2 NA
## 3 3 NA## Warning in min(AIC1_331$AIC, na.rm = T): no non-missing arguments to min;
## returning Inf## Error in h(simpleError(msg, call)) :
## error in evaluating the argument 'object' in selecting a method for function 'summary': object 'nls_331.' not foundsummary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
332 - Great Plains Steppe
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 191 153.88
## 2 190 153.65 1 0.2322 0.2871 0.592712
## 3 189 148.00 1 5.6458 7.2097 0.007896 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 616.7039
## 2 2 618.4110
## 3 3 613.1482##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.18048 1.41956 0.127 0.89896
## phi 0.02621 0.03238 0.809 0.41926
## alpha 0.74146 0.24974 2.969 0.00338 **
## A 4.26017 1.31891 3.230 0.00146 **
## k 73.68572 23.20341 3.176 0.00175 **
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8849 on 189 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 5.194e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 189 148.00
## 2 188 145.01 1 2.9971 3.8857 0.05017 .
## 3 188 146.37 0 0.0000
## 4 187 144.47 1 1.8955 2.4534 0.11896
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 613.1482
## 2 3a 611.1793
## 3 3b 612.9933
## 4 3c 612.4646##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.26182 1.44312 0.181 0.85623
## phi 0.02425 0.03187 0.761 0.44773
## alpha 0.71025 0.25011 2.840 0.00501 **
## A 5.21576 2.01157 2.593 0.01027 *
## k 142.59856 82.12245 1.736 0.08413 .
## p 0.07450 0.03154 2.362 0.01918 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8782 on 188 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.058e-06
## (1 observation deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.87217, p-value = 9.607e-12
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.9762, p-value = 0.04814
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1120 row(s) containing missing values (geom_path).
plotting 2
341 - Intermountain Semi-desert & Desert
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
342 - Intermountain Semi-Desert
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 112 64.762
## 2 111 64.757 1 0.0050 0.0086 0.9262372
## 3 110 58.505 1 6.2514 11.7538 0.0008554 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 281.0948
## 2 2 283.0859
## 3 3 273.4110##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.664552 6.035725 0.441 0.659744
## phi -0.001369 0.049853 -0.027 0.978140
## alpha 0.882084 0.226696 3.891 0.000171 ***
## A 3.485949 2.914237 1.196 0.234199
## k 119.510749 46.346783 2.579 0.011240 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7293 on 110 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 2.475e-06
## (6 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_342, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_342, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 110 58.505
## 2 109 58.268 1 0.23753 0.4443 0.5064
## model AIC
## 1 3 273.4110
## 2 3a 274.9432
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.664552 6.035725 0.441 0.659744
## phi -0.001369 0.049853 -0.027 0.978140
## alpha 0.882084 0.226696 3.891 0.000171 ***
## A 3.485949 2.914237 1.196 0.234199
## k 119.510749 46.346783 2.579 0.011240 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7293 on 110 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 2.475e-06
## (6 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9253, p-value = 7.497e-06
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.5772, p-value = 0.009961
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 5 rows containing missing values (geom_point).## Warning: Removed 1241 row(s) containing missing values (geom_path).
plotting 2
411 - Everglades
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M211 - Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6726 4643.6
## 2 6725 4629.4 1 14.19 20.609 5.732e-06 ***
## 3 6724 4292.9 1 336.46 526.988 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 24169.66
## 2 2 24151.07
## 3 3 23645.34##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.561222 0.172710 3.249 0.001162 **
## phi 0.013736 0.003985 3.447 0.000571 ***
## alpha 0.652872 0.026435 24.697 < 2e-16 ***
## A 3.091045 0.104099 29.693 < 2e-16 ***
## k 3.644354 0.420767 8.661 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.799 on 6724 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 4.867e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 6724 4292.9
## 2 6723 4289.6 1 3.3301 5.2192 0.0223693 *
## 3 6723 4292.7 0 0.0000
## 4 6722 4284.7 1 7.9936 12.5406 0.0004009 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 23645.34
## 2 3a 23642.11
## 3 3b 23647.01
## 4 3c 23636.47##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.551036 0.171824 3.207 0.001348 **
## phi 0.013969 0.003984 3.506 0.000457 ***
## alpha 0.652137 0.026377 24.724 < 2e-16 ***
## A 3.030047 0.102675 29.511 < 2e-16 ***
## k 11.469522 2.059551 5.569 2.66e-08 ***
## p 0.434424 0.064905 6.693 2.36e-11 ***
## s 1.831085 0.364824 5.019 5.33e-07 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.7984 on 6722 degrees of freedom
##
## Number of iterations to convergence: 10
## Achieved convergence tolerance: 3.677e-06summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
predict and plot
## Warning: Removed 1108 row(s) containing missing values (geom_path).
plotting 2
M221 - Eastern Broadleaf Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 8031 11168
## 2 8030 11166 1 1.823 1.3112 0.2522
## 3 8029 10911 1 254.340 187.1516 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 35928.80
## 2 2 35929.49
## 3 3 35746.37##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.745755 0.108485 -6.874 6.70e-12 ***
## phi -0.004038 0.005576 -0.724 0.469
## alpha 0.706276 0.049224 14.348 < 2e-16 ***
## A 5.088125 0.146783 34.664 < 2e-16 ***
## k 13.204274 1.640594 8.048 9.58e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.166 on 8029 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 5.523e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M221, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M221, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 35746.37
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.745755 0.108485 -6.874 6.70e-12 ***
## phi -0.004038 0.005576 -0.724 0.469
## alpha 0.706276 0.049224 14.348 < 2e-16 ***
## A 5.088125 0.146783 34.664 < 2e-16 ***
## k 13.204274 1.640594 8.048 9.58e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.166 on 8029 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 5.523e-06summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
predict and plot
## Warning: Removed 982 row(s) containing missing values (geom_path).
plotting 2
M223 - Ozark Broadleaf Forest Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 880 1100.5
## 2 879 1098.3 1 2.201 1.7611 0.1848
## 3 878 1056.4 1 41.982 34.8937 4.976e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 3499.284
## 2 2 3499.516
## 3 3 3467.103##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.75733 1.43670 1.919 0.0553 .
## phi -0.04134 0.02218 -1.864 0.0627 .
## alpha 0.90068 0.14067 6.403 2.48e-10 ***
## A 2.04112 0.39553 5.160 3.05e-07 ***
## k 14.57963 6.08332 2.397 0.0168 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.097 on 878 degrees of freedom
##
## Number of iterations to convergence: 13
## Achieved convergence tolerance: 8.927e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M223, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M223, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 3467.103
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 2.75733 1.43670 1.919 0.0553 .
## phi -0.04134 0.02218 -1.864 0.0627 .
## alpha 0.90068 0.14067 6.403 2.48e-10 ***
## A 2.04112 0.39553 5.160 3.05e-07 ***
## k 14.57963 6.08332 2.397 0.0168 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.097 on 878 degrees of freedom
##
## Number of iterations to convergence: 13
## Achieved convergence tolerance: 8.927e-06summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.96591, p-value = 1.666e-13
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.1402, p-value = 0.03234
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1175 row(s) containing missing values (geom_path).
plotting 2
M231 - Ouachita Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 984 1380.5
## 2 983 1362.3 1 18.220 13.147 0.0003028 ***
## 3 982 1318.1 1 44.205 32.933 1.27e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4121.784
## 2 2 4110.671
## 3 3 4080.114##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.59998 1.21002 1.322 0.1864
## phi 0.06577 0.02558 2.571 0.0103 *
## alpha 0.72924 0.11866 6.146 1.16e-09 ***
## A 2.18045 0.41408 5.266 1.72e-07 ***
## k 3.19690 1.48910 2.147 0.0320 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.159 on 982 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 5.242e-06
## (1 observation deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "a", sep = "")), data = G_M231, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M231, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## model AIC
## 1 3 4080.114
## 2 3a NA
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.59998 1.21002 1.322 0.1864
## phi 0.06577 0.02558 2.571 0.0103 *
## alpha 0.72924 0.11866 6.146 1.16e-09 ***
## A 2.18045 0.41408 5.266 1.72e-07 ***
## k 3.19690 1.48910 2.147 0.0320 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.159 on 982 degrees of freedom
##
## Number of iterations to convergence: 15
## Achieved convergence tolerance: 5.242e-06
## (1 observation deleted due to missingness)summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93491, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -6.094, p-value = 1.101e-09
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1218 row(s) containing missing values (geom_path).
plotting 2
M242 - Cascade Mixed Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3153 5953.4
## 2 3152 5925.9 1 27.58 14.672 0.0001304 ***
## 3 3151 5607.9 1 318.01 178.685 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 14761.88
## 2 2 14749.22
## 3 3 14577.14##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.16625 0.29272 -3.984 6.93e-05 ***
## phi -0.05013 0.01571 -3.192 0.00143 **
## alpha 0.97943 0.06623 14.788 < 2e-16 ***
## A 8.24024 0.70911 11.621 < 2e-16 ***
## k 87.52750 6.33761 13.811 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.334 on 3151 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 1.72e-06
## (23 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 3151 5607.9
## 2 3150 5532.1 1 75.782 43.151 5.906e-11 ***
## 3 3150 5563.3 0 0.000
## 4 3149 5509.3 1 53.962 30.843 3.030e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 14577.14
## 2 3a 14536.20
## 3 3b 14553.96
## 4 3c 14525.20##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.16019 0.29038 -3.995 6.60e-05 ***
## phi -0.05181 0.01563 -3.315 0.000927 ***
## alpha 0.95984 0.06610 14.521 < 2e-16 ***
## A 7.38315 0.65191 11.325 < 2e-16 ***
## k 126.92667 9.30383 13.642 < 2e-16 ***
## p 0.27138 0.02639 10.282 < 2e-16 ***
## s 1.97560 0.26706 7.398 1.77e-13 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.323 on 3149 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 4.255e-06
## (23 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.93721, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.8569, p-value = 0.0001148
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 9 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 184 row(s) containing missing values (geom_path).
plotting 2
M261 - Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1944 2736.4
## 2 1943 2648.3 1 88.031 64.585 1.588e-15 ***
## 3 1942 2525.2 1 123.122 94.687 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 8215.337
## 2 2 8153.671
## 3 3 8062.982##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.99592 0.19686 -10.139 <2e-16 ***
## phi 0.12817 0.01434 8.939 <2e-16 ***
## alpha 0.83851 0.07880 10.641 <2e-16 ***
## A 13.36137 1.07860 12.388 <2e-16 ***
## k 137.33346 12.64614 10.860 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.14 on 1942 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 2.946e-06
## (16 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1942 2525.2
## 2 1941 2504.1 1 21.118 16.369 5.417e-05 ***
## 3 1941 2521.5 0 0.000
## 4 1940 2491.7 1 29.802 23.204 1.570e-06 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 8062.982
## 2 3a 8048.631
## 3 3b 8062.103
## 4 3c 8040.954##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.98380 0.19705 -10.067 < 2e-16 ***
## phi 0.12772 0.01428 8.947 < 2e-16 ***
## alpha 0.84477 0.07666 11.020 < 2e-16 ***
## A 11.14578 1.06201 10.495 < 2e-16 ***
## k 130.79304 13.97929 9.356 < 2e-16 ***
## p 0.16266 0.03221 5.050 4.84e-07 ***
## s 1.64253 0.23847 6.888 7.63e-12 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.133 on 1940 degrees of freedom
##
## Number of iterations to convergence: 5
## Achieved convergence tolerance: 2.264e-06
## (16 observations deleted due to missingness)summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9432, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -1.559, p-value = 0.119
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 9 rows containing missing values (geom_point).
plotting 2
M262 - Califormia Coastal Range = Coniferous Forest - Open woodland Shrub Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
M313 - Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 359 156.17
## 2 358 152.35 1 3.8252 8.9887 0.002906 **
## 3 357 137.98 1 14.3704 37.1815 2.796e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 822.1395
## 2 2 815.1626
## 3 3 781.2972##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -2.05106 0.34195 -5.998 4.90e-09 ***
## phi 0.05371 0.02230 2.409 0.0165 *
## alpha 0.81606 0.11897 6.859 3.06e-11 ***
## A 11.88674 2.36632 5.023 8.04e-07 ***
## k 196.34353 47.26084 4.154 4.08e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6217 on 357 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 5.533e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M313, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 357 137.98
## 2 356 137.27 1 0.70579 1.8304 0.1769
## model AIC
## 1 3 781.2972
## 2 3a 781.4408
## 3 3b 780.7006
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s +
## B_plt_t1_MgHa^s))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -2.036e+00 3.455e-01 -5.893 8.78e-09 ***
## phi 5.390e-02 2.227e-02 2.420 0.016 *
## alpha 8.125e-01 1.191e-01 6.820 3.91e-11 ***
## A 1.617e+02 1.587e+03 0.102 0.919
## k 1.958e+04 3.033e+05 0.065 0.949
## s 7.028e-01 1.607e-01 4.373 1.61e-05 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.6203 on 356 degrees of freedom
##
## Number of iterations to convergence: 13
## Achieved convergence tolerance: 8.71e-07summary
- add p model: fits
- add s model: fits
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.9698, p-value = 7.756e-07
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = 0.15594, p-value = 0.8761
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1183 row(s) containing missing values (geom_path).
plotting 2
M331 - Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1708 1232.3
## 2 1707 1210.2 1 22.129 31.213 2.686e-08 ***
## 3 1706 1119.5 1 90.733 138.270 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 4418.632
## 2 2 4389.628
## 3 3 4258.286##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.83743 1.05906 0.791 0.429
## phi 0.09908 0.01294 7.656 3.18e-14 ***
## alpha 0.72719 0.05181 14.036 < 2e-16 ***
## A 1.83390 0.36253 5.059 4.68e-07 ***
## k 34.99648 5.27052 6.640 4.20e-11 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8101 on 1706 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 8.455e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M331, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M331, :
## step factor 0.000488281 reduced below 'minFactor' of 0.000976562
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1706 1119.5
## 2 1705 1093.8 1 25.708 40.074 3.119e-10 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 4258.286
## 2 3a 4220.536
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 1.19875 1.18352 1.013 0.3113
## phi 0.10174 0.01276 7.971 2.85e-15 ***
## alpha 0.73681 0.05033 14.640 < 2e-16 ***
## A 4.97281 2.69680 1.844 0.0654 .
## k 594.83063 458.19282 1.298 0.1944
## p 0.11960 0.05369 2.228 0.0260 *
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8009 on 1705 degrees of freedom
##
## Number of iterations to convergence: 8
## Achieved convergence tolerance: 7.114e-07summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90717, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -5.55, p-value = 2.857e-08
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1091 row(s) containing missing values (geom_path).
plotting 2
M332 - Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2623 2316.2
## 2 2622 2310.0 1 6.161 6.9935 0.00823 **
## 3 2621 2046.0 1 264.004 338.1952 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 8369.361
## 2 2 8364.366
## 3 3 8047.671##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.26356 0.30114 -4.196 2.81e-05 ***
## phi 0.03588 0.01468 2.445 0.0146 *
## alpha 0.95036 0.04423 21.489 < 2e-16 ***
## A 5.98323 0.62056 9.642 < 2e-16 ***
## k 82.21307 7.86354 10.455 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8835 on 2621 degrees of freedom
##
## Number of iterations to convergence: 11
## Achieved convergence tolerance: 8.229e-06
## (23 observations deleted due to missingness)summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M332, :
## number of iterations exceeded maximum of 50
## Error in numericDeriv(form[[3L]], names(ind), env, central = nDcentral) :
## Missing value or an infinity produced when evaluating the model
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 2621 2046.0
## 2 2620 1909.3 1 136.75 187.65 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 8047.671
## 2 3a 7868.020
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -1.32429 0.27714 -4.778 1.86e-06 ***
## phi 0.02949 0.01413 2.087 0.037 *
## alpha 0.92831 0.04313 21.521 < 2e-16 ***
## A 43.24977 35.26058 1.227 0.220
## k 2281.03867 2086.52516 1.093 0.274
## p 0.02976 0.02304 1.292 0.197
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8537 on 2620 degrees of freedom
##
## Number of iterations to convergence: 13
## Achieved convergence tolerance: 7.946e-06
## (23 observations deleted due to missingness)summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.90185, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -7.4344, p-value = 1.051e-13
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 11 rows containing missing values (geom_point).## Warning: Removed 1 rows containing missing values (geom_pointrange).## Warning: Removed 1001 row(s) containing missing values (geom_path).
plotting 2
M333 - Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1672 1976.4
## 2 1671 1975.6 1 0.811 0.686 0.4076
## 3 1670 1717.1 1 258.478 251.384 <2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 6547.760
## 2 2 6549.072
## 3 3 6316.200##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 0.664811 0.956615 0.695 0.487
## phi 0.002048 0.018148 0.113 0.910
## alpha 1.010251 0.055489 18.206 < 2e-16 ***
## A 4.270907 0.794280 5.377 8.64e-08 ***
## k 45.022078 4.833813 9.314 < 2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 1.014 on 1670 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 4.412e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Error in nls(get(paste("fg_", Mod.Sel1, "b", sep = "")), data = G_M333, :
## number of iterations exceeded maximum of 50
## Error in nls(get(paste("fg_", Mod.Sel1, "c", sep = "")), data = G_M333, :
## number of iterations exceeded maximum of 50
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 1670 1717.1
## 2 1669 1625.4 1 91.741 94.203 < 2.2e-16 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 3 6316.20
## 2 3a 6226.23
## 3 3b NA
## 4 3c NA##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A +
## ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge 4.912e-01 8.705e-01 0.564 0.572686
## phi 6.384e-03 1.762e-02 0.362 0.717251
## alpha 9.850e-01 5.397e-02 18.250 < 2e-16 ***
## A 9.893e+00 2.669e+00 3.707 0.000217 ***
## k 4.404e+02 1.477e+02 2.981 0.002917 **
## p 1.201e-01 2.004e-02 5.992 2.53e-09 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.9868 on 1669 degrees of freedom
##
## Number of iterations to convergence: 9
## Achieved convergence tolerance: 8.68e-06summary
- add p model: fits
- add s model: does not fit
- add s+p model: does not fit
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.91305, p-value < 2.2e-16
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -3.8628, p-value = 0.0001121
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 925 row(s) containing missing values (geom_path).
plotting 2
M334 - Black Hills Coniferous Forest
model selection 1
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 359 279.44
## 2 358 279.00 1 0.4466 0.5731 0.4495
## 3 357 256.62 1 22.3752 31.1276 4.782e-08 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## model AIC
## 1 1 993.7167
## 2 2 995.1377
## 3 3 966.8751##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.30924 1.46617 -0.211 0.833073
## phi 0.01064 0.03218 0.331 0.741036
## alpha 0.76868 0.12107 6.349 6.58e-10 ***
## A 2.55364 0.81480 3.134 0.001867 **
## k 36.20697 10.23649 3.537 0.000458 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8478 on 357 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 9.941e-06summary
- simple model: fits
- phi model: fits
- phi-alpha model: fits
model selection 2
## Analysis of Variance Table
##
## Model 1: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)
## Model 2: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa/(k + B_plt_t1_MgHa)))
## Model 3: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s))
## Model 4: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) * (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * (p * A + ((1 - p) * A * B_plt_t1_MgHa^s/(k^s + B_plt_t1_MgHa^s)))
## Res.Df Res.Sum Sq Df Sum Sq F value Pr(>F)
## 1 357 256.62
## 2 356 256.50 1 0.11926 0.1655 0.6844
## 3 356 256.62 0 0.00000
## 4 355 255.90 1 0.71939 0.9980 0.3185
## model AIC
## 1 3 966.8751
## 2 3a 968.7068
## 3 3b 968.8749
## 4 3c 969.8587##
## Formula: G_obs_TreeInc_MgHaYr ~ (1 + (MEASTIME_avg - 1990) * ge/100) *
## (1 + phi * DeltaPDSI) * (1 - alpha * B_L_prop) * A * B_plt_t1_MgHa/(k +
## B_plt_t1_MgHa)
##
## Parameters:
## Estimate Std. Error t value Pr(>|t|)
## ge -0.30924 1.46617 -0.211 0.833073
## phi 0.01064 0.03218 0.331 0.741036
## alpha 0.76868 0.12107 6.349 6.58e-10 ***
## A 2.55364 0.81480 3.134 0.001867 **
## k 36.20697 10.23649 3.537 0.000458 ***
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.8478 on 357 degrees of freedom
##
## Number of iterations to convergence: 6
## Achieved convergence tolerance: 9.941e-06summary
- add p model: fits
- add s model: fits
- add s+p model: fits
plot residuals
##
## ------
## Shapiro-Wilk normality test
##
## data: stdres
## W = 0.92291, p-value = 1.076e-12
##
##
## ------##
## Runs Test
##
## data: as.factor(run)
## Standard Normal = -2.1853, p-value = 0.02887
## alternative hypothesis: two.sidedpredict and plot
## Warning: Removed 1264 row(s) containing missing values (geom_path).
plotting 2
M341 - Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow
model selection 1
summary
- simple model: does not fit
- phi model: does not fit
- phi-alpha model: does not fit
model selection 2
summary
- add p model: does not fit
- add s model: does not fit
- add s+p model: does not fit
plot residuals
## [1] "cannot plot residuals"predict and plot
## [1] "cannot plot data with prediction"plotting 2
Fitted parameters
Best / selected models by ecoprovince
| Code | Ecoregion | Sel.Mod |
|---|---|---|
| 211 | Northeastern Mixed Forest | 3a |
| 212 | Laurentian Mixed Forest | 3a |
| 221 | Eastern Broadleaf Forest | 3a |
| 222 | Midwest Broadleaf Forest | 3a |
| 223 | Central Interior Broadleaf Forest | 3 |
| 231 | Southeastern Mixed Forest | 3a |
| 232 | Outer Coastal Plain Mixed Forest | 3c |
| 234 | Lower Mississippi Riverine Forest | 3b |
| 242 | Pacific Lowland Mixed Forest | 3a |
| 251 | Prairie Parkland (Temperate) | 3a |
| 255 | Prairie Parkland (Subtropical) | NA |
| 261 | California Coastal Chaparral Forest and Shrub | NA |
| 262 | California Dry Steppe | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | NA |
| 313 | Colorado Plateau Semi-Desert | 3c |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | NA |
| 321 | Chihuahuan Semi-Desert | NA |
| 322 | American Semidesert and Desert | NA |
| 331 | Great Plains/Palouse Dry Steppe | NA |
| 332 | Great Plains Steppe | 3a |
| 341 | Intermountain Semi-Desert and Desert | NA |
| 342 | Intermountain Semi-Desert | 3 |
| 411 | Everglades | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | 3c |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | 3 |
| M223 | Ozark Broadleaf Forest Meadow | 3 |
| M231 | Ouachita Mixed Forest | 3 |
| M242 | Cascade Mixed Forest | 3c |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | 3c |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | 3b |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | 3a |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3a |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | 3a |
| M334 | Black Hills Coniferous Forest | 3 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | NA |
table by ecoprovince
| Code | Ecoregion | region | n.obs | n.plots | ge | ge.2.5 | ge.97.5 | phi | phi.2.5 | phi.97.5 | alpha | alpha.2.5 | alpha.97.5 | A | A.2.5 | A.97.5 | k | k.2.5 | k.97.5 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 211 | Northeastern Mixed Forest | east | 6806 | 2847 | 0.0032341 | -0.2756589 | 0.2821270 | 0.0196353 | 0.0111317 | 0.0281389 | 0.6304287 | 0.5726594 | 0.6881979 | 3.741260 | 3.5207886 | 3.961732 | 13.699719 | 9.654695e+00 | 1.774474e+01 |
| 212 | Laurentian Mixed Forest | east | 18775 | 8891 | 0.5875552 | 0.3473638 | 0.8277467 | 0.0296065 | 0.0242962 | 0.0349169 | 0.8146466 | 0.7753388 | 0.8539544 | 3.134793 | 2.9862625 | 3.283323 | 29.206857 | 2.538519e+01 | 3.302852e+01 |
| 221 | Eastern Broadleaf Forest | east | 7170 | 3490 | -1.4353661 | -1.5984164 | -1.2723159 | 0.0067019 | -0.0020867 | 0.0154906 | 0.6856822 | 0.6180803 | 0.7532841 | 7.601341 | 6.8772003 | 8.325482 | 99.330652 | 6.020173e+01 | 1.384596e+02 |
| 222 | Midwest Broadleaf Forest | east | 4877 | 2401 | -0.3832030 | -0.7169445 | -0.0494615 | 0.0181604 | 0.0039591 | 0.0323617 | 0.7924866 | 0.7179678 | 0.8670053 | 6.608906 | 5.8836321 | 7.334179 | 112.210544 | 8.332827e+01 | 1.410928e+02 |
| 223 | Central Interior Broadleaf Forest | east | 8783 | 3725 | -1.3866092 | -1.5488155 | -1.2244028 | -0.0223289 | -0.0329539 | -0.0117039 | 0.6406604 | 0.5695074 | 0.7118133 | 6.472890 | 6.1175357 | 6.828244 | 42.043717 | 3.673232e+01 | 4.735511e+01 |
| 231 | Southeastern Mixed Forest | east | 12347 | 5691 | -0.1868506 | -0.3779020 | 0.0042008 | -0.0021302 | -0.0101573 | 0.0058968 | 0.8401828 | 0.8007650 | 0.8796007 | 5.596113 | 5.3550385 | 5.837187 | 8.774600 | 5.594570e+00 | 1.195463e+01 |
| 232 | Outer Coastal Plain Mixed Forest | east | 12470 | 6101 | -0.2904340 | -0.5045303 | -0.0763378 | -0.0008326 | -0.0096675 | 0.0080024 | 0.8287948 | 0.7872407 | 0.8703488 | 5.513232 | 5.1838221 | 5.842643 | 24.180337 | 1.997348e+01 | 2.838720e+01 |
| 234 | Lower Mississippi Riverine Forest | east | 1265 | 714 | 1.6092105 | -0.5934506 | 3.8118716 | -0.0257637 | -0.0665282 | 0.0150008 | 0.7689237 | 0.6117706 | 0.9260769 | 4.138424 | 2.3170892 | 5.959759 | 11.645585 | -5.094672e-01 | 2.380064e+01 |
| 242 | Pacific Lowland Mixed Forest | pacific | 81 | 81 | -0.9525826 | -3.5499334 | 1.6447682 | 0.0699013 | -0.0266063 | 0.1664088 | 0.8122504 | 0.3308180 | 1.2936827 | 22.297206 | -32.5184393 | 77.112850 | 1188.987146 | -3.496157e+03 | 5.874131e+03 |
| 251 | Prairie Parkland (Temperate) | east | 1797 | 809 | -0.8248859 | -1.3168379 | -0.3329340 | 0.0263597 | 0.0060061 | 0.0467134 | 0.3946292 | 0.2215338 | 0.5677246 | 19.869740 | -28.7842324 | 68.523713 | 1228.269336 | -2.646294e+03 | 5.102833e+03 |
| 255 | Prairie Parkland (Subtropical) | pacific | 663 | 293 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 261 | California Coastal Chaparral Forest and Shrub | pacific | 24 | 24 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 262 | California Dry Steppe | pacific | 0 | 0 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 263 | California Coastal Steppe - Mixed Forest and Redwood Forest | pacific | 155 | 155 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 313 | Colorado Plateau Semi-Desert | interior west | 215 | 215 | -1.1547223 | -3.0100569 | 0.7006123 | -0.0954482 | -0.2296346 | 0.0387382 | 0.8440010 | 0.3810746 | 1.3069274 | 2.685375 | 0.8808844 | 4.489866 | 109.843632 | 5.821653e+01 | 1.614707e+02 |
| 315 | Southwest Plateau and Plains Dry Steppe and Shrub | interior west | 4 | 4 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 321 | Chihuahuan Semi-Desert | interior west | 9 | 9 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 322 | American Semidesert and Desert | interior west | 3 | 3 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 331 | Great Plains/Palouse Dry Steppe | interior west | 304 | 240 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 332 | Great Plains Steppe | interior west | 195 | 106 | 0.2618211 | -2.5849626 | 3.1086047 | 0.0242467 | -0.0386217 | 0.0871152 | 0.7102473 | 0.2168739 | 1.2036208 | 5.215762 | 1.2476133 | 9.183912 | 142.598563 | -1.940133e+01 | 3.045985e+02 |
| 341 | Intermountain Semi-Desert and Desert | interior west | 62 | 62 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| 342 | Intermountain Semi-Desert | interior west | 121 | 120 | 2.6645524 | -9.2968369 | 14.6259417 | -0.0013691 | -0.1001661 | 0.0974279 | 0.8820840 | 0.4328260 | 1.3313421 | 3.485949 | -2.2893846 | 9.261282 | 119.510749 | 2.766230e+01 | 2.113592e+02 |
| 411 | Everglades | east | 93 | 61 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M211 | Adirondack-New England Mixed forest - Coniferous Forest - Alpine Meadow | east | 6729 | 2989 | 0.5510365 | 0.2142071 | 0.8878658 | 0.0139686 | 0.0061589 | 0.0217782 | 0.6521370 | 0.6004297 | 0.7038444 | 3.030047 | 2.8287707 | 3.231323 | 11.469522 | 7.432149e+00 | 1.550689e+01 |
| M221 | Central Appalachian Broadleaf Forest - Coniferous Forest - Meadow | east | 8034 | 3700 | -0.7457552 | -0.9584146 | -0.5330959 | -0.0040380 | -0.0149685 | 0.0068926 | 0.7062759 | 0.6097832 | 0.8027687 | 5.088126 | 4.8003928 | 5.375858 | 13.204274 | 9.988285e+00 | 1.642026e+01 |
| M223 | Ozark Broadleaf Forest Meadow | east | 883 | 343 | 2.7573280 | -0.0624472 | 5.5771032 | -0.0413414 | -0.0848804 | 0.0021975 | 0.9006835 | 0.6245979 | 1.1767690 | 2.041119 | 1.2648198 | 2.817419 | 14.579634 | 2.640085e+00 | 2.651918e+01 |
| M231 | Ouachita Mixed Forest | east | 988 | 481 | 1.5999846 | -0.7745286 | 3.9744977 | 0.0657658 | 0.0155696 | 0.1159619 | 0.7292396 | 0.4963788 | 0.9621003 | 2.180454 | 1.3678621 | 2.993047 | 3.196898 | 2.747197e-01 | 6.119077e+00 |
| M242 | Cascade Mixed Forest | pacific | 3179 | 3176 | -1.1601936 | -1.7295372 | -0.5908500 | -0.0518086 | -0.0824529 | -0.0211644 | 0.9598361 | 0.8302333 | 1.0894389 | 7.383150 | 6.1049325 | 8.661366 | 126.926665 | 1.086845e+02 | 1.451689e+02 |
| M261 | Sierran Steppe - Mixed Forest - Coniferous Forest - Alpine Meadow | pacific | 1963 | 1963 | -1.9838043 | -2.3702620 | -1.5973466 | 0.1277165 | 0.0997199 | 0.1557131 | 0.8447735 | 0.6944352 | 0.9951119 | 11.145784 | 9.0629800 | 13.228589 | 130.793041 | 1.033770e+02 | 1.582090e+02 |
| M262 | California Coastal Range Coniferous Forest - Open Woodland - Shrub - Meadow | interior west | 19 | 19 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
| M313 | Arizona-New Mexico Mountains Semi-Desert - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 362 | 362 | -2.0360162 | -2.7154342 | -1.3565981 | 0.0539041 | 0.0101067 | 0.0977015 | 0.8124616 | 0.5781913 | 1.0467319 | 161.727835 | -2958.5278536 | 3281.983523 | 19582.557845 | -5.768110e+05 | 6.159761e+05 |
| M331 | Southern Rocky Mountain Steppe - Open Woodland - Coniferous Forest - Alpine Meadow | interior west | 1711 | 1711 | 1.1987530 | -1.1225524 | 3.5200584 | 0.1017445 | 0.0767105 | 0.1267786 | 0.7368088 | 0.6380970 | 0.8355206 | 4.972806 | -0.3165882 | 10.262201 | 594.830630 | -3.038487e+02 | 1.493510e+03 |
| M332 | Middle Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 2649 | 2648 | -1.3242877 | -1.8677141 | -0.7808613 | 0.0294913 | 0.0017781 | 0.0572045 | 0.9283088 | 0.8437272 | 1.0128904 | 43.249774 | -25.8916364 | 112.391184 | 2281.038666 | -1.810366e+03 | 6.372443e+03 |
| M333 | Northern Rocky Mountain Steppe - Coniferous Forest - Alpine Meadow | interior west | 1675 | 1675 | 0.4911505 | -1.2162515 | 2.1985525 | 0.0063836 | -0.0281853 | 0.0409525 | 0.9849811 | 0.8791243 | 1.0908378 | 9.892989 | 4.6586997 | 15.127278 | 440.407307 | 1.506162e+02 | 7.301984e+02 |
| M334 | Black Hills Coniferous Forest | interior west | 362 | 170 | -0.3092380 | -3.1926440 | 2.5741681 | 0.0106444 | -0.0526491 | 0.0739379 | 0.7686805 | 0.5305895 | 1.0067715 | 2.553637 | 0.9512291 | 4.156044 | 36.206965 | 1.607556e+01 | 5.633837e+01 |
| M341 | Nevada-Utah Mountains Semi-Desert - Coniferous Forest - Alpine Meadow | interior west | 213 | 213 | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA | NA |
plot ge
map
## OGR data source with driver: ESRI Shapefile
## Source: "C:\Users\hogan.jaaron\Dropbox\FIA_R\Mapping\S_USA.EcoMapProvinces\S_USA.EcoMapProvinces.shp", layer: "S_USA.EcoMapProvinces"
## with 37 features
## It has 17 fields
## Integer64 fields read as strings: PROVINCE_ PROVINCE_I
map2
## Warning: package 'ggnewscale' was built under R version 4.2.1## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, : font
## family not found in Windows font database
plot phi (effect of DeltaPDSI)
plot alpha (biomass growth compensation effect)
plot A (asymptote of forest biomass growth in Mg/ha/yr)
## Warning: Removed 15 rows containing missing values (geom_point).
plot k (stand biomass at half biomss G in Mg/ha)
## Warning: Removed 14 rows containing missing values (geom_point).
Caclulations - weighted averages
ge (stand biomass growth enhancement factor in % 2000-2021)
## region weighted.ge
## 1 entire US -0.2989889
## 2 pacific -1.3450706
## 3 east -0.1801957
## 4 interior west -0.1751151phi (effect of DeltaPDSI)
## region weighted.phi
## 1 entire US 0.012449470
## 2 pacific 0.016132330
## 3 east 0.007881616
## 4 interior west 0.035209433alpha (biomass growth compensation effect)
## region weighted.alpha
## 1 entire US 0.7672651
## 2 pacific 0.8384614
## 3 east 0.7492007
## 4 interior west 0.8146180A (asymptote of forest biomass growth in Mg/ha/yr)
## region weighted.A
## 1 entire US 8.405587
## 2 pacific 8.280768
## 3 east 5.188456
## 4 interior west 26.483097K (stand biomass at half biomss G in Mg/ha)
## region weighted.k
## 1 entire US 325.45977
## 2 pacific 132.84852
## 3 east 55.87903
## 4 interior west 1977.47017Calculations - weighted averages subsetted to 15 ecoprovinces
- ecoprovince codes: 211, 212, 221, 223, 231, 232, 234, 251, M211, M221, M223, M231, M242, M261, M332
ge
## region weighted.ge
## 1 entire US -0.3737310
## 2 pacific -1.4747972
## 3 east -0.1682194
## 4 interior west -1.3242877phi
## region weighted.phi
## 1 entire US 0.009535741
## 2 pacific 0.016766534
## 3 east 0.007273321
## 4 interior west 0.029491284alpha
## region weighted.alpha
## 1 entire US 0.7759548
## 2 pacific 0.9158844
## 3 east 0.7477370
## 4 interior west 0.9283088